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Acta Mechanica Solida Sinica

, Volume 23, Issue 5, pp 420–427 | Cite as

Dynamic Characteristics in Incompressible Hyperelastic Cylindrical Membranes

  • Datian Niu
  • Xuegang Yuan
  • Changjun Cheng
  • Jiusheng Ren
Article

Abstract

In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.

Key words

incompressible hyperelastic material cylindrical membrane dynamical characteristic nonlinear periodic oscillation 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  • Datian Niu
    • 1
  • Xuegang Yuan
    • 1
  • Changjun Cheng
    • 2
  • Jiusheng Ren
    • 2
  1. 1.School of ScienceDalian Nationalities UniversityDalianChina
  2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina

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